Clean the leeks well. Start by cutting off and discarding the root ends and thick, dark green parts. Cut the leeks in half lengthwise and rinse each half under cold water, pulling apart the layers to remove any grit that's tucked inside. Roughly chop the white and light green parts only, which will yield about 5 cups.
Melt the butter over medium heat in a large soup pot. Add the leeks and garlic and cook, stirring regularly, until soft and wilted, about 10 minutes. Adjust the heat as necessary so as not to brown.
Add the potatoes, broth, bay leaves, thyme, salt and pepper to pot and bring to a boil. Cover and turn the heat down to low. Simmer for 15 minutes, or until the potatoes are very soft.
Remove the thyme sprig and bay leaves.
Purée the soup with a hand-held immersion blender until smooth.
NOTE: If using a standard blender to purée the soup, don't fill the jar more than halfway. Leave the hole in the lid open and cover loosely with a dishtowel to allow the heat to escape. Pour blended soup into a clean pot.
Add the heavy cream and bring to a simmer. Taste and adjust seasoning with salt and pepper. If soup is too thin, simmer until thickened. If it's too thick, add water or broth to thin it out.
Garnish with shaved Parmesan and Joyloop Pepper Mix.